The understanding of multiphase multi-component transport in capillary porous media plays an important role in scientific and engineering disciplines such as the petroleum and environmental industries. The two most commonly used tools to model multiphase multi-component flow are finite difference and finite volume methods. While these are well-established methods, they either fail to provide stability on unstructured meshes or they yield low order approximation. In this thesis, a presentation of both fully coupled and sequential discontinuous Galerkin (DG) formulations for the multiphase multi-component flow is given. Two physical models are examined: the black oil model and the CO2 sequestration model. The attractive attribute of using DG is that it permits the use of unstructured meshes while maintaining high order accuracy. Furthermore, the method can be structured to ensure mass conservation, which is another appealing feature when one is dealing with fluid dynamic problems.